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Properties

Label 17.9
Level 17
Weight 9
Dimension 88
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 216
Trace bound 0

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(216\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(17))\).

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

Trace form

\( 88 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} + O(q^{10}) \) \( 88 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} + 21496 q^{10} - 27968 q^{11} + 172024 q^{12} + 19984 q^{13} - 141320 q^{14} - 272144 q^{15} + 134896 q^{17} + 770032 q^{18} + 82816 q^{19} - 602120 q^{20} - 1209728 q^{21} - 694280 q^{22} + 176224 q^{23} + 2453128 q^{24} - 1715920 q^{25} - 925352 q^{26} + 2939320 q^{27} + 4516072 q^{28} - 275528 q^{29} - 7843400 q^{30} - 5352712 q^{31} - 4838880 q^{32} + 9334968 q^{34} + 8050928 q^{35} + 16654136 q^{36} + 4647416 q^{37} + 8405200 q^{38} - 19334424 q^{39} - 49015240 q^{40} - 8023472 q^{41} + 19462408 q^{42} + 21418088 q^{43} + 55649944 q^{44} + 12876632 q^{45} - 42199192 q^{46} - 28631408 q^{47} - 56707840 q^{48} - 14300136 q^{49} + 16156760 q^{51} + 58777584 q^{52} + 72829624 q^{53} - 12773160 q^{54} - 47916072 q^{55} - 42610448 q^{56} + 8039072 q^{57} + 43505424 q^{58} - 3667112 q^{59} + 24554384 q^{60} - 170296 q^{61} + 25385392 q^{62} - 94112864 q^{63} + 6935048 q^{64} - 125391128 q^{65} - 220878144 q^{66} + 225348832 q^{68} + 176211296 q^{69} + 87384336 q^{70} + 40919176 q^{71} + 234186544 q^{72} + 167466192 q^{73} + 111150568 q^{74} - 125599592 q^{75} - 61416384 q^{76} - 212184488 q^{77} - 541008288 q^{78} - 176854504 q^{79} - 279231000 q^{80} + 92322504 q^{81} + 91580672 q^{82} + 462895984 q^{83} - 504357528 q^{85} - 617697952 q^{86} + 70542376 q^{87} + 711198008 q^{88} + 426540736 q^{89} + 1253929784 q^{90} + 566661608 q^{91} + 461913448 q^{92} - 38907432 q^{93} - 713174760 q^{94} - 741593960 q^{95} - 1781388112 q^{96} - 482346152 q^{97} - 1202501264 q^{98} + 147226040 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(17))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
17.9.e \(\chi_{17}(3, \cdot)\) 17.9.e.a 88 8